Among the many concepts in numerical analysis for differential equations, "stiffness" appears one of the least straightforward ones to define and characterize. This talk contrasts various forms of stiff limits and associated model problems, and establishes how these different shapes of stiffness manifest in the numerical solution of both ordinary and partial differential equations. Then it is presented which hierarchies of additional order conditions can be formulated that ensure that various classes of Runge-Kutta methods retain their desired convergence rates in the eye of different forms of stiffness.